What is the derivative of x(x-1)^2 ?

The derivative of x(x-1)^2 is 3x^2-4x+1

What is the first derivative of x(x-1)^2 ?

The first derivative of x(x-1)^2 is 3x^2-4x+1

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derivative of

x (x - 1)^{2}

3 x^{2} - 4 x + 1

Solution steps

\frac{d}{d x} (x (x - 1)^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x - 1)^{2}

= \frac{d x}{d x} (x - 1)^{2} + \frac{d}{d x} ((x - 1)^{2}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 1)^{2}) = 2 (x - 1)

= 1 \cdot (x - 1)^{2} + 2 (x - 1) x

Simplify

1 \cdot (x - 1)^{2} + 2 (x - 1) x : 3 x^{2} - 4 x + 1

= 3 x^{2} - 4 x + 1

\int 3 x sin (2 x) d x

\frac{d}{d x} (\frac{2 x cos ( x ^{2} )}{1 + sin ( x ^{2} )})

f^{^{'}} (x) = x^{3}

\frac{1}{x + 5}

\frac{d}{d x} (x + i y (x))

What is the derivative of x(x-1)^2 ?
The derivative of x(x-1)^2 is 3x^2-4x+1
What is the first derivative of x(x-1)^2 ?
The first derivative of x(x-1)^2 is 3x^2-4x+1